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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 23, 31-44, 2016
https://doi.org/10.5194/npg-23-31-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
29 Feb 2016
A sequential Bayesian approach for the estimation of the age–depth relationship of the Dome Fuji ice core
Shin'ya Nakano1,2, Kazue Suzuki1, Kenji Kawamura3,2, Frédéric Parrenin4, and Tomoyuki Higuchi1,2 1The Institute of Statistical Mathematics, Research Organization of Information and Systems, Tachikawa, 190-8562, Japan
2School of Multidisciplinary Science, SOKENDAI, Hayama, 240-0115, Japan
3National Institute of Polar Research, Research Organization of Information and Systems, Tachikawa, 190-8518, Japan
4Laboratoire de Glaciologie et Géophysique de l'Environnement, 38041, Grenoble, France
Abstract. A technique for estimating the age–depth relationship in an ice core and evaluating its uncertainty is presented. The age–depth relationship is determined by the accumulation of snow at the site of the ice core and the thinning process as a result of the deformation of ice layers. However, since neither the accumulation rate nor the thinning process is fully known, it is essential to incorporate observational information into a model that describes the accumulation and thinning processes. In the proposed technique, the age as a function of depth is estimated by making use of age markers and δ18O data. The age markers provide reliable age information at several depths. The data of δ18O are used as a proxy of the temperature for estimating the accumulation rate. The estimation is achieved using the particle Markov chain Monte Carlo (PMCMC) method, which is a combination of the sequential Monte Carlo (SMC) method and the Markov chain Monte Carlo method. In this hybrid method, the posterior distributions for the parameters in the models for the accumulation and thinning process are computed using the Metropolis method, in which the likelihood is obtained with the SMC method, and the posterior distribution for the age as a function of depth is obtained by collecting the samples generated by the SMC method with Metropolis iterations. The use of this PMCMC method enables us to estimate the age–depth relationship without assuming either linearity or Gaussianity. The performance of the proposed technique is demonstrated by applying it to ice core data from Dome Fuji in Antarctica.

Citation: Nakano, S., Suzuki, K., Kawamura, K., Parrenin, F., and Higuchi, T.: A sequential Bayesian approach for the estimation of the age–depth relationship of the Dome Fuji ice core, Nonlin. Processes Geophys., 23, 31-44, https://doi.org/10.5194/npg-23-31-2016, 2016.
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This paper proposes a technique for dating an ice core. The proposed technique employs a hybrid method combining the sequential Monte Carlo method and the Markov chain Monte Carlo method, which is referred to as the particle Markov chain Monte Carlo method. The sequential Monte Carlo method, which is also known as the particle filter, is widely used for nonlinear time-series analysis. This paper demonstrates the usefulness of the approach in time-series analysis for dating an ice core.
This paper proposes a technique for dating an ice core. The proposed technique employs a hybrid...
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